The exact solution is obtained for a propagator describing x-ray propagation through a refractive parabolic medium. Such a medium arises in compound many-element refractive x-ray lenses that are used in synchrotron radiation sources. The solution obtained allows one to analyze such lenses in detail to predict their operation in particular applications (beam focusing, microobject imaging, and Fourier transform).
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Victor G. Kohn (2002) studied this question.
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